Lectures for the Summer School in honour of Prof. J.M. Araujo, Oporto, Portugal, 23rd-29th August 1998.

Dr Joan Adler,


Technion- Israel Institute of Technology,

Haifa, Israel


The first part of this lecture is partly based on a talk given at the First Israeli Scientific Visualization Conference, Jerusalem, 1995, and published in the Conference Proceedings. Detailed references to the software mentioned below can be found at the Technion Computational Physics group homepage and our graphics page.

ELEMENTARY PHYSICS: In the teaching regime, computerised visualization is nothing but a natural extension of lecture demonstrations. When teaching elementary mechanics and electricity, numerous lecture demonstrations are made, to explain effects and to hold the students' interest. (Computer visualization is also useful here, but it is far from the only tool and may not even be the best.)

MODERN PHYSICS: Once students of science and engineering begin the study of so-called `Modern Physics' and study atoms and quantum mechanics and their applications to condensed matter physics, it is difficult to show anything significant in a demonstration. Some topics, such as radioactivity are dangerous to demonstrate. Other aspects, such as crystal structures can be modelled with mechanical models. Three examples of mechanical visualization are ball and stick models of different lattices (at the Technion these sit in our library and can be borrowed like books), spinning wooden models photographed to represent different hydrogen atom wavefunctions, and a box of glass balls used to demonstrate amorphous and crystalline structures. A classic set of photographs (presented by H. E. White in ``Introduction to Atomic Spectra'', 1934) of spinning wooden models is reproduced below.


Photographic representations of electron cloud made from spinning wooden models for several energy states of the H atom.

Despite the elegance of this set of photographs from the mechanical models, computer visualization has a special role in these areas because with computer models the student can explore alone at his own pace. Perhaps, the computer routines will even encourage her/him to devote extra time to physics at the expense of other subjects/non-academic pursuits. The numerical solution of the Schroedinger equation is also a terrific way to introduce the ``shooting'' method algorithm for solving differential equations.

EXAMPLE: Schroedinger equation movie produced together with S. Goldberg, based on routines developed by Z. Salman and Y. ben Horin.

PRESENTATION QUALITY: When teaching today's university students, who have been exposed to Sesame Street and the MTV style of television, a reasonable quality of presentation is needed just to hold their attention. Some old strip films used in the past to illustrate animations of Schroedinger equation solutions today elicit the same amusement as a Laurel and Hardy movie. When we look at the excellent research visualizations that are now being done, it is unreasonable to settle for simple line drawings and primitive computer graphics for the students. However, I note that unless care is taken costs in manpower, hardware and software for interactive visualization on this scale can be enormous. The difficulty is to make interactive vizualization easy enough so that computer amateurs can do it, cheap enough so that univerisities can afford it and of sufficiently high quality that it is useful and impressive.

DEVELOPMENT OF ROUTINES: I like to use video presentation in large undergraduate classes, and to have the same routines (with their sourcecode) avaliable on an ftp server or diskette. The routines are developed as class projects in Computational Physics or Numerical Methods classes. The video presentation enables even the ``computationally challenged'' to use the teaching material with ease, and to be quite honest I use it myself to minimise technical problems, which are both bad for discipline and irritating. The early recording was made by holding a video camera at the screen; we are grateful to the Hebrew University Visualization Centre for assistance in making video recordings from their video disk at a later stage. Today, I use the TECHNION VISUALIZATION CENTRE to prepare the movies. (In fact I helped write the original proposal for this centre so that I could do exactly this.) On the technical side it should be noted that although the routines and the videos are made from the same original sourcecode, we often modify colors and linewidths for the video version. A sourcecode is always made available to the students as well and they are encouraged to look at the algorithms as well as just run the executable versions.

PGPLOT: One early approach to interactive visualization with sourcecode access was developed at the Technion for research and undergraduate teaching of physics. It is based on public domain PGPLOT, graphics both for preparing the video material and for the take-home routines. It is suited to simple pc or generic UNIX systems and although fortran based, can be linked with c routines. The Schroedinger video was made with PGPLOT, the timedependent equation being recorded frame by frame using a video disk in Jerusalem, and the time independent one using digital software at the Technion. PGPLOT is a library of routines that are incorporated into the c or fortran program, similar in concept to commercial libraries of subroutines such as DISSPLA, IMSL etc. It is an excellent ``first graphics'' even for students who then proceeed to OpenGL, because the conceptual approach of using graphic subroutines and commands inside a c program is similar.

ANIMATED SIMULATED ANNEALING: A description of another of our early routines, demonstrating the simulated annealing of argon atoms is given in

  • A. Silverman and J. Adler, ``Animated simulated annealing'', (1992) Computers in Physics, 6, 277-281. The programs from this paper can be found on our ftp site. This project was begun by A. Silverman, as the creation of a tool to enable him to monitor the simulated annealing of semiconductor models that he was carrying out for his Ph. D research.

    A GROUP EFFORT: Successive projects were based on this and substantial contributions were made by different graduate and undergraduate students at the Technion, with constant support from the Technion Computer Centre consulting group, especially, Drs C. Abulaffio and B. Pery. A partial listing of other applications is:

    1. Animated Simulated Annealing - A. Silverman.
    2. Time-dependent Schroedinger equation - Y. ben Horin.
    3. Kronig-Penney Model - I. Nofar.
    4. Metropolis and Wolff Algorithms - G. Baum.
    5. Quadrupoles - A. Manesseh.
    6. 3D Visualization - A. Gangardt.
    7. Crystal Growth - S. Kostianovsky
    8. Lattice Vibrations - M. Goldenberg
    9. Percolation - I. Braslavsky
    There are also optics, mechanics and elementary physics applications. All programs are avaliable on request from phr76ja@phjoan.technion.ac.il for non-commercial use in as-is condition, and recent ones are avaliable self service from the web page, either at the page for programs associated with publications or the page for recent class projects.

    GOOD INTERACTIVE ROUTINES: After grading more than 100 interactive routines since 1987 I have developed the following criteria for successful routines.

  • They must be as platform independent as possible, and use either public domain or site-licensed software that is easily installed and exists for both PC and UNIX. (As in, I neither make home visits nor allow students to bring in computers, since I think that students who understand their programs can also adapt them to a different machine.)
  • They must have interfaces that allow one to exit without rebooting the computer.
  • They must have adequate help files, demo versions and default parameter choices, so that everyone can run them first time.
  • I, and anyone passing by in the corridor must be able to run them without needing further instructions. (You may wish to modify this if your office is in a corner of the building where administrative staff pass by, my group's area is rather isolated and all departmental students are fair game for testing purposes.)
  • Within our local community the sources must be freely avaliable if they are teaching oriented and they must be avaliable to all future students of mine.

    MATLAB: Since the Technion is an engineering school, an engineering ethos dominates the campus and MATLAB has become popular. We have a site license for MATLAB at the Technion, but at other institutions this may not be the case. It is nicely suited for this type of interactive routine, moves well between PC and UNIX platforms and is user friendly to engineers. On the basis of since you can't beat them, join them I have been allowing students to do their projects in MATLAB for several years now. One of the nicest MATLAB routines is about to appear in the Computers in Physics Journal section as

  • T. Kidan, J. Adler and A. Ron, ``Computer simulations for atoms inside a laser light potential'', Computers in Physics, to appear. The matlab files for this paper are described on this site and are avaliable from our anonymous ftp site. An html version of the papers and figures can also be viewed.

  • To the previous page: Introduction.

    To the next page: Lecture 2.